In recent years, millions of children have been displaced, and evidence informing public policy for the welfare of migrants and recipient communities will be critical in the coming years. In this paper, we leverage cross-grade within-school variation on migrant share to understand the effect of the sudden influx of Venezuelan migrant children into the Peruvian school system. Our estimates show that as Venezuelan migrants enter Peruvian schools, parents of incumbent students react by transferring their children to higher-quality schools with fewer migrants. A ten-percentage-point increase in migrant exposure increases the probability of switching by 1.5 percentage points in primary and 1.1 percentage points in secondary schools. To understand the implications of this native flight on academic achievement, we employ a structural model that identifies students who switch schools because of migrants and compare their outcomes in the presence of migrants to a counterfactual scenario without migrants. Our findings reveal that switchers experience small gains (close to zero), albeit at a higher tuition cost, while students left behind are not negatively impacted. This suggests that native flight can serve as an adaptive strategy only for some students to mitigate the effects of the migrant influx, but generally brings no gains to students who switch schools. Moreover, it comes at a high cost.